Optical substructure and BCG offsets of Sunyaev–Zel’dovich and X-ray-selected galaxy clusters

We used optical imaging and spectroscopic data to derive substructure estimates for local Universe ($z < 0.11$) galaxy clusters from two different samples. The first was selected through the Sunyaev-Zel'dovich (SZ) effect by the Planck satellite and the second is an X-ray selected sample. In agreement to X-ray substructure estimates we found that the SZ systems have a larger fraction of substructure than the X-ray clusters. We have also found evidence that the higher mass regime of the SZ clusters, compared to the X-ray sample, explains the larger fraction of disturbed objects in the Planck data. Although we detect a redshift evolution in the substructure fraction, it is not sufficient to explain the different results between the higher-z SZ sample and the X-ray one. We have also verified a good agreement ($\sim$60$\%$) between the optical and X-ray substructure estimates. However, the best level of agreement is given by the substructure classification given by measures based on the brightest cluster galaxy (BCG), either the BCG$-$X-ray centroid offset, or the magnitude gap between the first and second BCGs. We advocate the use of those two parameters as the most reliable and cheap way to assess cluster dynamical state. We recommend an offset cut of $\sim$0.01$\times$R$_{500}$ to separate relaxed and disturbed clusters. Regarding the magnitude gap the separation can be done at $\Delta m_{12} = 1.0$. The central galaxy paradigm (CGP) may not be valid for $\sim$20$\%$ of relaxed massive clusters. This fraction increases to $\sim$60$\%$ for disturbed systems.